ABSTRACT
J. Aitchison and J. A. C. Brown summarized early methods of estimating the mean and variance of a two-parameter lognormal distribution. These methods included the method of moments, quantiles, a graphical method, and Finney's uniformly minimum variance unbiased (UMVU) estimators. This chapter considers lognormal distributions which have their lefthand limit at the origin, nonzero thresholds. It shows that estimation in the univariate distribution, whereas generalizations to multivariate distributions and distributions with a nonzero probability mass at the origin. UMVU estimation of regression equations for the bivariate log-normal distribution was treated by M. D. Mostafa and M. W. Mahmoud. Numerical computation shows that maximum likelihood estimates should be practically used because they are easier to calculate than UMVU estimates. G. E. P. Box and G. M. Jenkins systematically discussed the forecasting and model specification of the autoregressive integrated moving average process.
